Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×D1132 | C2 | semidirect |
| 3. #31826817 | C2 | semidirect |
| 4. #31826797 | C2 | semidirect |
| 5. #31826695 | C2 | semidirect |
| 6. #31826671 | C2 | semidirect |
| 7. #31826605 | C2 | semidirect |
| 8. C4×#17985379 | C2 | semidirect |
| 9. #31826530 | C2 | semidirect |
| 10. #103×D283 | C2 | semidirect |
| 11. #475×C283 | C2 | semidirect |
| 85. D1132 | SD16 | semidirect |
| 98. Q8×C283 | #41 | semidirect |
| 128. C283 | #3298 | semidirect |
| 134. #475 | D283 | semidirect |
| 213. Q8 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1132 | 2 |
| #31827118 | 2 |
| #31826817 | 2 |
| #31826797 | 2 |
| #31826695 | 2 |
| #31826671 | 2 |
| #31826605 | 2 |
| C4×#17985379 | 2 |
| #31826530 | 2 |
| #103×D283 | 2 |
| #475×C283 | 2 |
| #3298 | 283 |